The present invention is directed generally to a method and apparatus for removing solids from a solid-liquid mixture, as well as the removal of entrained gasses. Example solid-liquid mixtures include, e.g., drilling mud used in the oilfield industry, sewage, coal slurries, mining wastes, feed water for industrial applications, and other mixtures desired to be clarified. By way of one example, the method and apparatus of the present invention could be used alone or in combination with de-silters, de-sanders, de-gassers, shakers and shaker screens, and/or centrifuges used to treat drilling fluids in an oil field application.